Before stating the assumptions that the TBB stepsize must satisfy, we introduce some expressions that will be useful for the following results. We first decompose the gradient along an orthonormal basis of eigenvectors of \(A\) . Let \(\mathbf {v}_1, \dots , \mathbf {v}_n\)  be the (orthonormal) eigenvectors associated with the eigenvalues \(\lambda _1, \dots , \lambda _n\) . The gradient can be expressed as linear combination of these eigenvectors (cf., e.g., [1]})
\(g_k = \sum _{i=1}^n \gamma _{i}^{k} \, \mathbf {v}_i.\) 
